That strange sound you hear? It’s another collision of liberal orthodoxies. As usual, it is a clash between policies intended to help the working class and those that enshrine the tastes of the upper class.

In this case, that means the champions of affordable housing versus the preservationists. And the man in the middle is Bill de Blasio, the guy likely to be New York’s new mayor come January.

The Democratic candidate says expanding affordable housing is one of his biggest priorities. He vows to build 200,000 affordable units, using pension funds to construct some and a mix of law and tax breaks to get private developers to build the rest.

At the same time, de Blasio is a fan of landmarking. While visiting the New York Landmark Conservancy this summer, he talked up the importance of preservation.

But if a new study from the Real Estate Board of New York is right, de Blasio will have a tough time squaring that circle. According to this study, there have been exactly zero units of affordable housing built in landmarked districts in Manhattan since 2008 — and only five since 2003. That’s in contrast to the more than 8,000 new affordable housing units built borough-wide over the same decade.

It’s not just affordable housing, either. Of the 53,220 new, non-subsidized units built in Manhattan over the last 10 years, just 998 were in landmarked districts.

Why this is happening is no secret. The harder you make it to build, the less housing you will have. And less housing means higher prices for all.

This trend is likely to get even worse if preservationists succeed in getting more of Manhattan landmarked. Today, nearly 30% of the borough’s properties are covered — and in some neighborhoods (e.g., the Upper West Side and SoHo/Greenwich Village) the figure is double.

One reason for the explosion in landmarking is that advocates have moved from designating individual sites with specific historic import to defining whole neighborhoods as “landmark ­districts.”

So which is it, Bill? Will you go with the elite preservationists who would limit new housing even further by freezing even more of the city in amber? Or will you come down on the side of people who want to see more units of affordable housing built?

Our guess is that until he’s forced to, de Blasio’s going to continue to do just what he’s doing now: have it both ways.